Zlatan Ibrahimovic bagging four goals, while Juventus and Bayern Munich preserved their leads and FA Cup holders Arsenal were dumped out of the competition.
Manchester United and Manchester City must switch their focus from the Champions League to the Premier League when they meet at Old Trafford on Sunday in a derby that Louis van Gaal says will show whether United are true title contenders.
Atletico Madrid have been unable to repeat the magnificent achievements of last season in this campaign but can congratulate themselves on a job well done if they secure a lucrative Champions League berth on Saturday.
Liverpool handed their fiercest rivals a painful lesson on Thursday with a dominant 2-0 win over Manchester United in the first leg of a Europa League last-16 clash.
Real's Cristiano Ronaldo will be going in search of his third consecutive World Player of the Year award
Barcelona made a brisk start to the season with new coach Luis Enrique at the helm in place of Gerardo Martino and a host of additions to the squad, including midfielder Ivan Rakitic and goalkeeper Claudio Bravo.
Real Madrid and Barcelona pulled two points clear in La Liga when Cristiano Ronaldo set a club scoring record in Real's 3-0 stroll against Levante and Neymar hit four as Barca beat Rayo Vallecano 5-2 on Saturday.
Cristiano Ronaldo scored twice in his 150th European appearance to give Real Madrid a 3-1 victory at Borussia Dortmund, their first against them in Germany, and make it two wins out of two matches in their Champions League Group H.
Real Madrid forward Karim Benzema has not recovered sufficiently from a knee injury and has been left out of the squad for Tuesday's Champions League semi-final first leg at Juventus, the holders said on Monday.
A bullet header from Nicolas Otamendi put Valencia on course for a 3-1 victory over Eibar in La Liga on Sunday that boosted their hopes of claiming a Champions League place.
Real Madrid kept alive their hopes of overhauling La Liga leaders Barcelona when a James Rodriguez stunner set them on their way to a serene 3-0 home victory over struggling Almeria on Wednesday.
Liverpool's half-baked pre-season transfer dealings have come back to bite them with Brendan Rodgers admitting his side have lacked the quality to finish in the Premier League's top four.
Liverpool's half-baked pre-season transfer dealings have come back to bite them with Brendan Rodgers admitting his side have lacked the quality to finish in the Premier League's top four.
Now, Real Madrid have never won the Spanish treble and are fighting tooth and nail in La Liga to prevent arch-rivals Barcelona scooping Champions League and domestic league and Cup titles for a second time.
Valencia recaptured fourth place in La Liga from Sevilla when Sofiane Feghouli scored the pick of the goals in a 4-0 stroll at home to second-from-bottom Granada on Monday.
Manchester United's hopes of salvaging their season in the Europa League suffered a stinging setback when they lost 2-1 at Danish side Midtjylland in the first leg of their last-32 clash on Thursday.
Barcelona have been drawn to play Pep Guardiola's Bayern Munich in the Champions League semi-finals. The other last-four tie will see Juventus, in their first semi-final since 2003, take on Carlo Ancelotti's Real Madrid, the defending champions.
Lionel Messi scored one penalty and missed another as his double helped Barcelona sweep Levante aside in the second half in a 4-1 victory on Sunday to maintain their perfect La Liga start.
Valencia turned up the heat on Atletico Madrid in the fight for third place in La Liga when a 3-0 derby victory at home to Levante on Monday lifted the Singapore-owned club to within a point of the champions with seven games left.
Photos from the La Liga matches played on Sunday
Real Madrid's appeal against a yellow card shown to forward Cristiano Ronaldo in Wednesday's 2-0 La Liga win at Rayo Vallecano has been granted by the Spanish soccer federation (RFEF), the club said on Friday.
Valencia lost ground in the battle with Atletico Madrid and Sevilla for third place in La Liga when they conceded a late Aritz Aduriz equaliser in a bad-tempered 1-1 draw at Athletic Bilbao on Thursday.
Atletico Madrid made a typically aggressive start to lay the foundations for a 2-0 victory at home.
Barcelona's outlay of 20 million euros ($22 million) on Jeremy Mathieu last July prompted plenty of criticism but the France centre back has been worth his weight in gold in the La Liga leaders' last two outings.
James Rodriguez will return to Real Madrid's starting lineup for Sunday's La Liga game at home to Granada after being out for two months with a broken bone in his foot, coach Carlo Ancelotti said on Saturday.
The King's Cup final between record winners Barcelona and Athletic Bilbao on May 30 will be held at Barca's Nou Camp.
A summary of the results of the major European football league matches on the weekend.
Manchester United ended their one-year Champions League hiatus in emphatic style when Wayne Rooney struck a hat-trick in a 4-0 destruction of Club Bruges that sent the three-times winners through 7-1 on aggregate on Wednesday.
Spain became the first country to have five teams in the Champions League group stage in one season after Valencia squeezed past Monaco .
While it is unfair to blame the Wales winger for all of Real's recent woes, it cannot be denied that he appears to be struggling for form and confidence.
Antoine Griezmann and Yannick Carrasco each conjured moments of magic as Atletico Madrid recaptured top spot in La Liga from Barcelona with a hard-fought 2-0 victory at Celta Vigo on Sunday.
With five titles, Barca are now level with AC Milan on all-time UEFA Super Cup winners list
Luis Suarez played a part in all three of Barcelona's goals in a scrappy 3-1 victory at Granada.
Cristiano Ronaldo's bullet header helped Real Madrid to a 2-0 victory .
A Romelu Lukaku hat-trick in a 4-1 win for Everton at Young Boys and a thrilling 3-3 draw between Celtic and Inter Milan.
Real Madrid closed to within two points of La Liga leaders Barcelona after demolishing nine-man Rayo Vallecano 10-2 while Atletico Madrid missed a chance to seize top spot outright by losing 1-0 at Malaga.
Cristiano Ronaldo struck twice as a rampant Real Madrid side, featuring the most expensive strike force ever assembled, powered to a 2-0 win over Sevilla in an all-Spanish UEFA Super Cup on Tuesday.
Villarreal set up a King's Cup semis against Barca after Gerard Moreno gave them a 1-0 win
Neymar struck twice as Barca beat Atletico Madrid to reach the King's Cup semis
Real Madrid's Cristiano Ronaldo has been given a two-match ban following his dismissal for kicking out at an opponent during their La Liga clash with Cordoba last Saturday, the Spanish league said on Wednesday.